(1 point) In a large population the probability of someone being stricken with t

Question

(1 point) In a large population the probability of someone being stricken with the euphoric mental state "StatsOnMyMind-itis" is 0.105. The probability of a person with StatsOnMyMind-itis of getting into a stats-related conversation is 0.946. The probability of a person that doesn't have StatsOnMyMind-itis of getting into a stats-related conversation is 0.742 (a) What is the probability of having StatsOnMyMind-itis and ending up in a stats-related conversation? 0.09933 (b) What is the probability of having StatsOnMyMind-itis and not ending up in a stats-related conversation? 0.00567 (c) What is the probability of not having StatsOnMyMind-itis and ending up in a stats-related conversation?0.66409 (d) What is the probability of not having StatsOnMyMind-itis and not ending up in a stats-related conversation? 0.23091 (e) What is the probability of having StatsOnMyMind-itis given that you just ended up in a stats-related conversation? (f) What is the probability of not having StatsOnMyMind-itis given that you just ended up in a stats-related conversation? (g) What is the probability of having StatsOnMyMind-itis given that you have not ended up in a stats-related conversation? (h) What is the probability of not having StatsOnMyMind-itis given that you have not ended up in a stats-related conversation?

Explanation / Answer

P(StatsOnMyMind-itis) = 0.105

P( Conversation stats|StatsOnMyMind-itis) = 0.946

P( notConversation stats|StatsOnMyMind-itis) = 1-0.946 =0.054

P( Conversation stats|Doesn't StatsOnMyMind-itis) = 0.742

P( notConversation stats|Doesn't StatsOnMyMind-itis) = 1-0.742=0.258

e) P(StatsOnMyMind-itis | Conversation stats) =P( Conversation stats|StatsOnMyMind-itis) * P(StatsOnMyMind-itis)/P(Conversation stats) = 0.946 * 0.105 /( P(Conversation stats) )

=0.946 * 0.105 /(0.105*0.946+(1-0.105)*0.742) = 0.1301119

f)

P(notStatsOnMyMind-itis | Conversation stats) =P( Conversation stats|notStatsOnMyMind-itis) * P(nonStatsOnMyMind-itis)/P(Conversation stats) = 0.742 * 0.105 /( P(Conversation stats) )

=0.742 * 0.105 /(0.105*0.742+(1-0.105)*0.946) = 0.08426529

g) P(Statsonmymind | not stats related conv) = P(not Conv stats |Stats on mind) * P(Stats on mind) / P(not Conv stats)

=0.054*0.105/(0.105*0.054+(1-0.105)*0.258) = 0.02396652

h) P(notStatsonmymind | not stats related conv) = P(not Conv stats |notStats on mind) * P(notStats on mind) / P(not Conv stats)

=0.258 * 0.105 /(0.105*0.258+(1-0.105)*0.054) = 0.3591885

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!

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